Single layer neural network circuit for performing linearly separable and non-linearly separable logical operations

Abstract

A neural network provides both linearly separable and non-linearly separable logic operations, including the exclusive-or operation, on input signals in a single layer of circuits. The circuit weights the input signals with complex weights by multiplication and addition, and provides weighted signals to a neuron circuit (a neuron body or some a) which provides an output corresponding to the desired logical operation.

We claim: 
     
       1. A method for performing a non-linearly separable operation off three or more input electrical signals, comprising the steps of: receiving said input electrical signals in a single artificial neuron circuit;   weighting said input electrical signals with one or more complex weights to produce weighted signals, said complex weights each having a real component with a scalar value and an imaginary component with a scalar value, the scalar values of said real and imaginary components determining a type of nonlinearly separable operation on said three or more input electrical signal; and   generating an output electrical signal representative of the results of the non-linearly separable operation performed on said input electrical signals.   
     
     
       2. The method according to claim 1, further comprising the step of: thresholding said output signal to produce a signal equal either to logical 1 or to logical 0.   
     
     
       3. The method according to claim 4, wherein said weighting comprises forming one or more first signals proportional to the product of said input electrical signals and the scalar value of each of said real components and one or more second signals proportional to the product of said input signals and the scalar values of each of said imaginary components. 
     
     
       4. The method according to claim 3 further compromising: adding said first signals to produce added first signals;   adding said second signals to produce added second signals;   squaring said added first signals to produce a first squared signal;   squaring said added second signals to produce a second squared signal; and   adding said first and second squared signals to yield said output signal.   
     
     
       5. The method according to claim 1 wherein said predetermined logical process is exclusive OR. 
     
     
       6. The method according to claim 1 wherein said predetermined logical process is symmetry. 
     
     
       7. The method according to claim 1 wherein said predetermined logical process is NAND. 
     
     
       8. The method according to claim 1 wherein said predetermined logical process is OR. 
     
     
       9. The method according to claim 1 wherein said predetermined logical process is INVERTER. 
     
     
       10. The method of claim 1 wherein the complex weights have positive and negative values. 
     
     
       11. A single layer, single neuron, neural network circuit for performing a non-linearly separable predetermined logical process on one or more input signals comprising: means for applying the scalar values of the components of a predetermined complex weight to said one or more input signals to produce one or more weighted input signals, said predetermined complex weight being chosen so as to cause said circuit to perform the predetermined logical process;   means for adding said weighted input signals to produce a composite input signal;   means for squaring said composite input signal to produce a squared signal; and   means for thresholding said squared signal to produce an output signal representing the predetermined logical process.   
     
     
       12. The neural network according to claim 11, wherein said logical operation is quadrically separable. 
     
     
       13. The neural network circuit according to claim 11, wherein said predetermined logical process is an exclusive-or function. 
     
     
       14. A circuit for performing an exclusive-OR process on first and second electrical signals and outputting a resultant exclusive-OR electrical signal, comprising: first and second input means for applying said first and second electrical signals to said circuit;   multiplying means for electrically multiplying said applied first and second signals by first and second complex weighting signals, respectively, to produce first and second weighted inputs said complex weights being chosen to perform an exclusive-OR process on said input electrical signals;   summing means for electrically adding said first weighted input to said second weighted input to produce a sum signal; and   squaring means for electrically squaring said sum signal to produce said resultant exclusive-OR signal.   
     
     
       15. The circuit according to claim 14 wherein said first and second complex weighting signals represent the magnitudes of the real and imaginary portions of first and second complex numbers.